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van der Pol’s oscillator under delayed feedback. (English) Zbl 1235.70142
Summary: The effect of delayed feedback on oscillatory behaviour is investigated for the classical van der Pol oscillator. It is shown how the presence of delay can change the amplitude of limit cycle oscillations, or suppress them altogether. The result is compared to the conventional proportional-and-derivative feedback. The derivative-like effect of delay is also demonstrated in a modified equation where a delayed term provides the damping.

MSC:
70K99 Nonlinear dynamics in mechanics
34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
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